Facets on the convex hull of d-dimensional Brownian and Lévy motion.

For stationary, homogeneous Markov processes (viz., Lévy processes, including Brownian motion) in dimension d≥3, we establish an exact formula for the average number of (d-1)-dimensional facets that can be defined by d points on the process's path. This formula defines a universality class in that it is independent of the increments' distribution, and it admits a closed form when d=3, a case which is of particular interest for applications in biophysics, chemistry, and polymer science. We also show that the asymptotical average number of facets behaves as 〈F_{T}^{(d)}〉∼2[ln(T/Δt)]^{d-1}, where T is the total duration of the motion and Δt is the minimum time lapse separating points that define a facet.

• Publication year

  2017

• Venue

  Physical Review E

• Publication date

  2017-01-17

• Fields of study

  Mathematics, Physics, Chemistry, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.95.032129arXiv 1701.04753PMID 28415327
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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